全纯

本书暂定概念：尚未进入正式概念库。下面是本书给出的定义原文。

定义 · 8.1 复流形

首先，我们定义 ${\mathbb{C}}^m$ 上的全纯(holomorphic)（或解析）映射。复值函数 $f:{\mathbb{C}}^m\to \mathbb{C}$ 称为全纯的，是指 $f=f_1+\mathrm{i}{f}_2$ 对每个 $z^{\mu }=x^{\mu }+\mathrm{i}{y}^{\mu }$ 都满足柯西-黎曼关系，

$$\frac{\partial f_1}{\partial x^{\mu }}=\frac{\partial f_2}{\partial y^{\mu }}\frac{\partial f_2}{\partial x^{\mu }}=-\frac{\partial f_1}{\partial y^{\mu }}.\text{\hspace{1em}(8.1)}$$

英文原文

To begin with, we define a holomorphic (or analytic) map on ${\mathbb{C}}^m$ . A complex-valued function $f:{\mathbb{C}}^m\to \mathbb{C}$ is holomorphic if $f=f_1+\mathrm{i}{f}_2$ satisfies the Cauchy-Riemann relations for each $z^{\mu }=x^{\mu }+\mathrm{i}{y}^{\mu }$ ,

$$\frac{\partial f_1}{\partial x^{\mu }}=\frac{\partial f_2}{\partial y^{\mu }}\frac{\partial f_2}{\partial x^{\mu }}=-\frac{\partial f_1}{\partial y^{\mu }}.\text{\hspace{1em}(8.1)}$$

出处：8.1 复流形 · node a-e9a1c2dcc03266e55f1f53c6 · 源节点 SHA-256 7ce4f8db0bae859e…